Let x0 of type ι → ο be given.
Let x1 of type ι → ι → ι → ο be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ι → ι → ι → ι → ι be given.
Let x4 of type ι → ο be given.
Let x5 of type ι → ι → ι → ο be given.
Let x6 of type ι → ι be given.
Let x7 of type ι → ι → ι → ι → ι → ι be given.
Let x8 of type ι → ι be given.
Let x9 of type ι → ι → ι → ι be given.
The subproof is completed by applying and4E with ∀ x10 . x0 x10 ⟶ x4 (x8 x10), ∀ x10 x11 x12 . x0 x10 ⟶ x0 x11 ⟶ x1 x10 x11 x12 ⟶ x5 (x8 x10) (x8 x11) (x9 x10 x11 x12), ∀ x10 . x0 x10 ⟶ x9 x10 x10 (x2 x10) = x6 (x8 x10), ∀ x10 x11 x12 x13 x14 . x0 x10 ⟶ x0 x11 ⟶ x0 x12 ⟶ x1 x10 x11 x13 ⟶ x1 x11 x12 x14 ⟶ x9 x10 x12 (x3 x10 x11 x12 x14 x13) = x7 (x8 x10) (x8 x11) (x8 x12) (x9 x11 x12 x14) (x9 x10 x11 x13).